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MR1286798 (95h:11075) 11K31 (11K55 28D99)
Lesigne, E.; Mauduit, C.; Mossé, B. Le théorème ergodique le long d'une suite $q$-multiplicative. (French) [The ergodic theorem along a $q$-multiplicative sequence] Compositio Math. 93 (1994), no. 1, 49–79.
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